Related papers: Positive Lyapunov exponents for Hamiltonian linear…

A recently developed method for the calculation of Lyapunov exponents of dynamical systems is described. The method is applicable whenever the linearized dynamics is Hamiltonian. By utilizing the exponential representation of symplectic…

We show that for a class of $C^2$ quasiperiodic potentials and for any Diophantine frequency, the Lyapunov exponents of the corresponding Schr\"odinger cocycles are uniformly positive and weak H\"older continuous as function of energies. As…

Criteria for the simplicity of the Lyapunov spectra of linear cocycles have been found by Furstenberg, Guivarc'h-Raugi, Gol'dsheid-Margulis and, more recently, Bonatti-Viana and Avila-Viana. In all the cases, the authors consider cocycles…

Given a linear cocycle over an ergodic homeomorphism on a compact metric space, we show that the existence of a uniform gap between the $p$-th and $(p+1)$-th Lyapunov exponent on a $C^0$-neighbourhood implies the existence of a dominated…

We construct an example of a Hamiltonian flow $f^t$ on a $4$-dimensional smooth manifold $\mathcal{M}$ which after being restricted to an energy surface $\mathcal{M}_e$ demonstrates essential coexistence of regular and chaotic dynamics that…

In this paper we establish uniform large deviations estimates of exponential type and H\"older continuity of the Lyapunov exponents for random non-invertible cocycles with constant rank.

The covariant Lyapunov analysis is generalised to systems attached to deterministic thermal reservoirs that create a heat current across the system and perturb it away from equilibrium. The change in the Lyapunov exponents as a function of…

We show that linear analytic cocycles where all Lyapunov exponents are negative infinite are nilpotent. For such one-frequency cocycles we show that they can be analytically conjugated to an upper triangular cocycle or a Jordan normal form.…

We show that, for any compact surface, there is a residual (dense $G_\delta$) set of $C^1$ area preserving diffeomorphisms which either are Anosov or have zero Lyapunov exponents a.e. This result was announced by R. Mane, but no proof was…

We prove that small nonlinear perturbations of random linear dynamics admitting a tempered exponential dichotomy have a random version of the shadowing property. As a consequence, if the exponential dichotomy is uniform, we get that the…

We present a set of results concerning the existence of Lyapunov-Krasovskii functionals for classes of nonlinear switched systems with time-delay. In particular, we first present a result for positive systems that relaxes conditions…

In this paper we prove the continuity of all Lyapunov exponents, as well as the continuity of the Oseledets decomposition, for a class of irreducible cocycles over strongly mixing Markov shifts. Moreover, gaps in the Lyapunov spectrum lead…

We study the relationship between the Lyapunov exponents of the geodesic flow of a closed negatively curved manifold and the geometry of the manifold. We show that if each periodic orbit of the geodesic flow has exactly one Lyapunov…

In hyperbolic dynamics, a well-known result is: every hyperbolic Lyapunov stable set, is attracting; it's natural to wonder if this result is maintained in the sectional-hyperbolic dynamics. This question is still open, although some…

This paper is concerned with the Lyapunov spectrum for measurable cocycles over an ergodic pmp system taking values in semi-simple real Lie groups. We prove simplicity of the Lyapunov spectrum and its continuity under certain perturbations…

We show that any measurable solution of the cohomological equation for a H\"older linear cocycle over a hyperbolic system coincides almost everywhere with a H\"older solution. More generally, we show that every measurable invariant…

We extend the results of arXiv:2206.08295v2 by showing that any homothety in $\mathbb T^2$ is homotopic to a non-uniformly hyperbolic ergodic area preserving map, provided that its degree is at least $5^2$. We also address other small…

This paper is concerned with stochastic Hamiltonian systems which model a class of open dynamical systems subject to random external forces. Their dynamics are governed by Ito stochastic differential equations whose structure is specified…

In this paper we study a classification of linear systems on Lie groups with respect to the conjugacy of the corresponding flows. We also describe stability according to Lyapunov exponents.

We scrutinize the reliability of covariant and Gram-Schmidt Lyapunov vectors for capturing hydrodynamic Lyapunov modes (HLMs) in one-dimensional Hamiltonian lattices. We show that,in contrast with previous claims, HLMs do exist for any…